Explicit wave action conservation for water waves on vertically sheared flows

Surface Waves on Vertically Sheared Flows: Approximate Dispersion Relations

Assuming linear wave theory for [1974] for deep water. We then obtain solutions waves riding on a weak current of O(c) compared to to the general problem to 0(1⁄2) (reproducing the the wave phase speed, an approximate dispersion result of Skop [1987]) and to 0(1⁄22). In section 3 relation is developed to 0(1⁄2 2 ) for arbitrary curwe apply the method to linear, cosine, and 1/7rent U(z) in water...

Boussinesq Waves on Vertically Sheared Currents

Interaction of finite-amplitude waves with vertically sheared current fields

A computationally efficient numerical method is developed to investigate nonlinear interactions between steep surface gravity waves and depth-varying ocean currents. The free-surface boundary conditions are used to derive a coupled set of equations that are integrated in time for the evolution of the free-surface elevation and tangential component of the fluid velocity at the free surface. The ...

Conservation Laws for Shallow Water Waves on a Sloping Beach

Shallow water waves are governed by a pair of non-linear partial differential equations. We transfer the associated homogeneous and non-homogeneous systems, (corresponding to constant and sloping depth, respectively), to the hodograph plane where we find all the non-simple wave solutions and construct infinitely many polynomial conservation laws. We also establish correspondence between conserv...

Energy exchange and wave action conservation for magnetohydrodynamic (MHD) waves in a general, slowly varying medium

Magnetohydrodynamic (MHD) waves in the solar wind and magnetosphere are propagated in a medium whose velocity is comparable to or greater than the wave velocity and which varies in both space and time. In the approximation where the scales of the time and space variation are long compared with the period and wavelength, the ray-tracing equations can be generalized and then include an additional...